Again and again genderist "thinkers" fall into the same trap.
Female and male bodied people definitely exist.
A thing called gender identity may exist, but certainly people who feel a thing they associate with the opposite sex to their own, or some partway state, exist.
So, we have the old definition of woman as adult human female, and a newer, conflicting definition of woman as a mental gender.
Also undeniably, there are people claiming to be "women" under both definitions.
But the thing that the first group are, and the thing that the second group feel, are manifestly different things. There is no connection, no continuity between these two concepts. So there is no basis to claim, as genderists are, that the second group are somehow a more - real? authorative? - version of the first group.
In short, the second you try to claim "womanhood" based on gender identity, you immediately and unavoidably undefine it based on sex, and thereby make all pre-existing rights and access of "women" invalid for your new group because by your own acceptance that trans women are women, you are also defining these pre-existing rights as based on something that is not womanhood.
So regardless of whether trans women are women or not, they have no claim on the rights and accesses of "women" that were based on the needs of people of the female sex, either because trans women are not women, or because if trans women are women, then these rights and accesses for people of the female sex are not rights and accesses of women, because women are no longer defined as female.
However you cut it, the rights and accesses of the female sex belong to, and only to, the female sex.
That's what genderists never understand. These rights and accesses are not about the name Woman, they are and always have been about the people who happened to bear that name at the time.